<header>
    什么是逆？如何计算等
</header>
<p>
    <span class="title">
        定义
    </span>
    n级方阵A称为可逆的，如果有n级方阵B，使得
    <span class="oneline">
        AB = BA = E ，
    </span>
    这里E是n级单位矩阵。
</p>
<p>
    上面的矩阵B就是矩阵A的逆(反过来也成立),记作A<sup>-1</sup>=B，当然，一个矩阵有逆矩阵的前提一定是其本身是一个方阵。
</p>
<h2>
    如何求一个矩阵的逆矩阵？
</h2>
<p>
    先来看一个定义。
</p>
<p>
    <span class="title">
        定义
    </span>
    设A<sub>ij</sub>是矩阵
    <span class="oneline">
        A =
        <code>
            ["matrix",[
                [["rightBottom","a","11"],["rightBottom","a","12"],"...",["rightBottom","a","1n"]],
                [["rightBottom","a","21"],["rightBottom","a","22"],"...",["rightBottom","a","2n"]],
                ["⁝","⁝"," ","⁝"],
                [["rightBottom","a","n1"],["rightBottom","a","n2"],"...",["rightBottom","a","nn"]]
            ]]
        </code>
    </span>
    中元素a<sub>ij</sub>的代数余子式，矩阵
    <span class="oneline">
        A<sup>*</sup> =
        <code>
            ["matrix",[
                [["rightBottom","A","11"],["rightBottom","A","21"],"...",["rightBottom","A","n1"]],
                [["rightBottom","A","12"],["rightBottom","A","22"],"...",["rightBottom","A","n2"]],
                ["⁝","⁝"," ","⁝"],
                [["rightBottom","A","1n"],["rightBottom","A","2n"],"...",["rightBottom","A","nn"]]
            ]]
        </code>
    </span>
    称为A的
    <span class="important">伴随矩阵</span>。
</p>
<p>
    下面我们就来说如何求解逆的。由行列式按一行（列）展开的公式可以知道：
    <span class="oneline">
        AA<sup>*</sup> = A<sup>*</sup>A =
        <code>
            ["matrix",[
                ["d","0","...","0"],
                ["0","d","...","0"],
                ["⁝","⁝"," ","⁝"],
                ["0","0","...","d"]
            ]]
        </code>
        = dE ，
    </span>
    其中d = |A|，
</p>
<p>
    如果d≠0，那么逆存在，且知道：
    <span class="oneline">
        A<sup>-1</sup> =
        <code>
            ["division","1","d"]
        </code>
        A<sup>*</sup>
    </span>
</p>
<h2>
    相关定理
</h2>
<p>
    <span class="title">
        定理
    </span>
    A是一个s×n矩阵，如果P是一个s×s可逆矩阵，Q是一个n×n可逆矩阵，那么
    <span class="oneline">
        秩(A) = 秩(PA) = 秩(AQ)
    </span>
</p>